Unearthly "pillars" have descended on the Earth, spawning monsters and death. Mankind had no idea how to fight them until the Norse god Odin arrived with his daughters, the Valkyries. They're schoolgirls in old-fashioned planes from the 1930s and 1940s (including a biplane), but they're more effective than trained pilots in the latest modern jet fighters.
This show hasn't received a huge amount of fan attention, but I enjoyed it.
It's more military than usual with these shows. (Yes, "flying schoolgirls are mankind's last line of defence in the fight against aliens" is a genre, e.g. Strike Witches.) There are planes, engineers, superior officers and male pilots who fly alongside the Valkyries as support and are quietly assumed to be expendable. The double-length first episode is all dour doom and battlefields and high-tech until its second half introduces the cute schoolgirls and reveals the show to be funnier and quirkier than that. (Tateyama Air Base is a home for oddballs with a relaxed attitude to the military way of life, although they all work very hard at their jobs.)
The show's main heroine is Claudia Bruford, a Valkyrie who's always been the only survivor of every mission she flies and has been nicknamed the Grim Reaper. She's in a dark place. Fortunately, her new comrades will help her snap out of it. Miyako is loud, lovable and not quite as empty-headed as the grumpy Azuzu would have you believe. (Azuzu is funny.) Then there's sweet, pink-haired Sonoka.
If I had to identify a weakness, it might be with inconsistent tone. It's a military show... but it doesn't feel very military most of the time. Tateyama Air Base is loose in both attitude and discipline, while the flashy modern jet fighters are coming second best to creaky old 1930s models. (You can also have a girl jumping out of her plane to attack a Pillar with her katana.) The air battles are exciting, but the twists and tactics in the finale aren't as clever as they think they are. In one episode, the death of a beloved character does serious psychological damage to a main cast member... and yet, in another episode, everyone strips to their swimwear for silly comedy nudity while a human supporting character dies repeatedly for laughs. (That's ep.4. It's so absurd that its existence is a problem for the show as a whole.)
Ep.1 has that bait-and-switch, fooling us into thinking we're watching a different kind of show. Ep.8.5 is a recap episode, of course including swimsuits and all the girls in the bath. Sometimes the show's serious, with death and mortal danger, and sometimes it's just cute girls goofing around.
That said, though, I'm not too fussed about all that. Even ep.4 might be amusing, if you're in the right mood. The show's serious mode works for me, with Claudia's reputation making me genuinely wonder in ep.1 if cute Miyako was about to die. The show has a death toll. Miyako sitting with the pilot who dies in ep.3 impressed me. It also has nifty ideas on the Norse gods and their motivations regarding the modern world and Ragnarok.
Then, at the same time, I also like the show's fluffier side. It's not just being mindlessly cute. Half the main cast are suffering from depression or worse at some point in the show, so their friends (living and dead) are helping them over that. Azuzu and Miyako made me laugh.
It's fun. It's exciting. It has magical alien monsters that turn into trees when you defeat them (which is cool and somehow more satisfying than just blowing stuff up). I think it's worth a watch.